China Airlines (not to be confused with Air China from China, this is the Taiwan-based airline and from personal experience is AWESOME) has a sale on DIRECT flights to Taipei.
Air New Zealand also has flights on sale direct for similar prices. Both will be shown below.
Both include full service, checked luggage.
Auckland to Taipei
Dates: 1 Feb 23 - 30 Sep 23
Cheapest: $1221 return
Auckland to Taipei (1 Feb - 30 Sep) from $1221